Number

313

313 is a prime, odd, a calendar year.

Arithmetic Number Binary Palindrome Cousin Prime Deficient Number Happy Number Odious Number Palindrome Pernicious Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Squarefree Twin Prime Year

Notable events — 313 AD

Undated Constantine and Licinius issue the Edict of Milan, legalising Christianity in the Roman Empire.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Historical context — 313 BC

Calendar year

Year 313 BC was a year of the pre-Julian Roman calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback Read the full article on Wikipedia →

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Wednesday
January 1, 313
Ended on: Wednesday
December 31, 313
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 310s
310–319
Century: 4th century
301–400
Millennium: 1st millennium
1–1000
Years ago: 1,713
1713 years before 2026.

In other calendars

Hebrew: 4073 / 4074 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Water zodiac:Rooster
Sexagenary cycle position 10 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 856 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 305 / 306 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 235 / 234 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 3
Digit sum: 7
Digit product: 9
Digital root: 7
Palindrome: Yes
Bit width: 9 bits
Recamán's sequence: a(622) = 313
Square (n²): 97,969
Cube (n³): 30,664,297
Divisor count: 2
σ(n) — sum of divisors: 314
φ(n) — Euler's totient: 312

Primality

313 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 313

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 313)

1 × 313

First multiples

313 · 626 (double) · 939 · 1,252 · 1,565 · 1,878 · 2,191 · 2,504 · 2,817 · 3,130

Sums & aliquot sequence

As a sum of two squares: 12² + 13²

As consecutive integers: 156 + 157

Representations

In words: three hundred thirteen
Ordinal: 313th
Roman numeral: CCCXIII
Binary: 100111001
Octal: 471
Hexadecimal: 0x139
Base64: ATk=
One's complement: 65,222 (16-bit)
Scientific notation: 3.13 × 10²

In other bases

ternary (3) 102121

quaternary (4) 10321

quinary (5) 2223

senary (6) 1241

septenary (7) 625

nonary (9) 377

undecimal (11) 265

duodecimal (12) 221

tridecimal (13) 1b1

tetradecimal (14) 185

pentadecimal (15) 15d

Palindromic in base 2, base 13

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹
Egyptian hieroglyphic: 𓍢𓍢𓍢𓎆𓏺𓏺𓏺
Greek (Milesian): τιγʹ
Mayan (base 20): 𝋯·𝋭
Chinese: 三百一十三
Chinese (financial): 參佰壹拾參

In other modern scripts

Eastern Arabic ٣١٣ Devanagari ३१३ Bengali ৩১৩ Tamil ௩௧௩ Thai ๓๑๓ Tibetan ༣༡༣ Khmer ៣១៣ Lao ໓໑໓ Burmese ၃၁၃

Digit at this position in famous constants

π — Pi (π): Digit 313 = 6
e — Euler's number (e): Digit 313 = 8
φ — Golden ratio (φ): Digit 313 = 4
√2 — Pythagoras's (√2): Digit 313 = 6
ln 2 — Natural log of 2: Digit 313 = 1
γ — Euler-Mascheroni (γ): Digit 313 = 7

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 311 (gap of 2)
Next prime: 317 (gap of 4)

Pair status: twin with 311, cousin with 317.

Unicode codepoint

Latin Capital Letter L With Acute

U+0139

Uppercase letter (Lu)

UTF-8 encoding: C4 B9 (2 bytes).

Lookup U+0139 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000139

RGB(0, 1, 57)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.57.

Address: 0.0.1.57
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.57

Unspecified address (0.0.0.0/8) — "this network" placeholder.

NANP area code 313

The number 313 is an active NANP area code (North American Numbering Plan).

Primary area: Detroit
Region: Michigan
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 313 ↗